theorem cases (a b: wff): $ a -> b $ > $ ~a -> b $ > $ b $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
contra |
(~b -> b) -> b |
| 2 |
|
hyp h1 |
a -> b |
| 3 |
|
con1 |
(~a -> b) -> ~b -> a |
| 4 |
|
hyp h2 |
~a -> b |
| 5 |
3, 4 |
ax_mp |
~b -> a |
| 6 |
2, 5 |
syl |
~b -> b |
| 7 |
1, 6 |
ax_mp |
b |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)